Hawking radiation emanating from a two-dimensional analogue of BTZ black holes is viewed as a tunnelling process. Two dimensional BTZ black holes (AdS(2) included) are treated as dynamical backgrounds in contrast to the standard methodology where the background geometry is fixed when evaluating Hawking radiation. This modification to the geometry gives rise to a nonthermal part in the radiation spectrum. Nonzero temperature of the extremal spinning BTZ black hole is found. The Bekenstein-Hawking area formula is easily derived for these dynamical geometries.